24 research outputs found
Arbitrage and deflators in illiquid markets
This paper presents a stochastic model for discrete-time trading in financial
markets where trading costs are given by convex cost functions and portfolios
are constrained by convex sets. The model does not assume the existence of a
cash account/numeraire. In addition to classical frictionless markets and
markets with transaction costs or bid-ask spreads, our framework covers markets
with nonlinear illiquidity effects for large instantaneous trades. In the
presence of nonlinearities, the classical notion of arbitrage turns out to have
two equally meaningful generalizations, a marginal and a scalable one. We study
their relations to state price deflators by analyzing two auxiliary market
models describing the local and global behavior of the cost functions and
constraints
Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis
Families of exact solutions are found to a nonlinear modification of the
Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM)
incorporates both transaction costs and the risk from a volatile portfolio.
Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM
equation. It gives us the possibility to describe an optimal system of
subalgebras and correspondingly the set of invariant solutions to the model. In
this way we can describe the complete set of possible reductions of the
nonlinear RAPM model. Reductions are given in the form of different second
order ordinary differential equations. In all cases we provide solutions to
these equations in an exact or parametric form. We discuss the properties of
these reductions and the corresponding invariant solutions.Comment: larger version with exact solutions, corrected typos, 13 pages,
Symposium on Optimal Stopping in Abo/Turku 200
General model selection estimation of a periodic regression with a Gaussian noise
This paper considers the problem of estimating a periodic function in a
continuous time regression model with an additive stationary gaussian noise
having unknown correlation function. A general model selection procedure on the
basis of arbitrary projective estimates, which does not need the knowledge of
the noise correlation function, is proposed. A non-asymptotic upper bound for
quadratic risk (oracle inequality) has been derived under mild conditions on
the noise. For the Ornstein-Uhlenbeck noise the risk upper bound is shown to be
uniform in the nuisance parameter. In the case of gaussian white noise the
constructed procedure has some advantages as compared with the procedure based
on the least squares estimates (LSE). The asymptotic minimaxity of the
estimates has been proved. The proposed model selection scheme is extended also
to the estimation problem based on the discrete data applicably to the
situation when high frequency sampling can not be provided
On the Existence of Shadow Prices
For utility maximization problems under proportional transaction costs, it
has been observed that the original market with transaction costs can sometimes
be replaced by a frictionless "shadow market" that yields the same optimal
strategy and utility. However, the question of whether or not this indeed holds
in generality has remained elusive so far. In this paper we present a
counterexample which shows that shadow prices may fail to exist. On the other
hand, we prove that short selling constraints are a sufficient condition to
warrant their existence, even in very general multi-currency market models with
possibly discontinuous bid-ask-spreads.Comment: 14 pages, 1 figure, to appear in "Finance and Stochastics
On martingale selectors of cone-valued processes.
International audienc
A super-replication theorem in Kabanov’s model of transaction costs
Proportional transaction costs, Foreign exchange markets, Efficient friction, Super-replication theorem, Primary 91B28, Secondary 60H30, Secondary 60G44, G10, G11, G13,
Hydrogenation of carbon oxides on ultrafine α-iron particles
The catalytic properties of ultrafine iron powders prepared by three different procedures in the hydrogenation of CO and CO2 were studied. Light olefins (ethylene and propylene) were found to be predominantly produced over catalysts prepared by the electrochemical method
Synthesis and properties of sorbents based on poly)ethyleneamine) pre-treated for nickel selectivity
Hydrogenation of carbon oxides on ultrafine α-iron particles
The catalytic properties of ultrafine iron powders prepared by three different procedures in the hydrogenation of CO and CO2 were studied. Light olefins (ethylene and propylene) were found to be predominantly produced over catalysts prepared by the electrochemical method